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Carleson Type Measures for Harmonic Mixed Norm Spaces with Application to Toeplitz Operators

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Chinese Annals of Mathematics,Series B 2013年第4期34卷 623-638页

作者： Zhangjian HU Xiaofen LV Department of Mathematics Huzhou Teachers College College of Mathematics and Science Xiamen University

Let Ω be a bounded domain in Rnwith a smooth boundary, and let h p,q be the space of all harmonic functions with a finite mixed norm. The authors first obtain an equivalent norm on h p,q, with which the definition of Carleson type measures for h p,q is obtained. And also, the authors obtain the boundedness of the Bergman projection on h p,q which turns out the dual space of h p,q. As an application, the authors characterize the boundedness(and compactness) of Toeplitz operators T μ on h p,q for those positive finite Borel measures μ.

关键词： Toeplitz 混合模空间谐波应用 Bergman投影类型松光滑边界

Plant N-acylethanolamines play a crucial role in defense and its variation in response to elevated CO_(2) and temperature in tomato

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Horticulture Research 2023年第1期10卷 207-219页

作者： Zhangjian HU Junying Shi Shuxian Feng Xiaodan Wu Shujun Shao Kai Shi Hainan Institute Zhejiang UniversityYazhou Bay Science and Technology CitySanya 572025China Department of Horticulture Zhejiang University310058China Analysis Center of Agrobiology and Environmental Science Zhejiang UniversityHangzhou310058China

The ubiquitous lipid-derived molecules N-acylethanolamines(NAEs)have multiple immune functions in mammals,but their roles and mechanisms in plant defense response during changing environment remain largely unclear.Here,we found that exogenous NAE18:0 and NAE18:2 promoted defense against the necrotrophic pathogen Botrytis cinerea but suppressed defense to the hemi-biotrophic pathogen Pseudomonas syringae pv.tomato(Pst)DC3000 in tomato.The knocking-down and overexpression function analysis of the pathogen-responsive NAE synthetic gene PHOSPHOLIPASE Dγ(PLDγ)and hydrolytic gene FATTY ACID AMID HYDROLASE 1(FAAH1)revealed that the NAE pathway is crucial for plant defense response.Using exogenous applications and SA-abolished NahG plants,we unveiled the antagonistic relationship between NAE and SA in plant defense response.Elevated CO_(2) and temperature significantly changed the NAE pathway in response to pathogens,while inhibition of the NAE pathway led to the alternation of environment-mediated defense variations against Pst DC3000 in tomato,indicating that NAE pathway is associated with plant defense variations in response to elevated CO_(2) and temperature.The results herein reveal a new function of NAE in plant defense,and its involvement in environment-mediated defense variation in tomato.These findings shed light on the NAE-based plant defense,which may have relevance to crop disease management in future changing climate.

关键词： elevated defense Plant

Composition operators between Bloch-type spaces in the polydisc

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Science China Mathematics 2005年第Z1期48卷 268-282页

作者： hu zhangjian huzhou Teachers College Huzhou313000China

We characterize those holomorphic mappings ψ from the polydisc Dn in Cn to itself for which the induced composition operators Cψ are bounded (or compact) from the Bloch-type space Bω to βμ (respectively, from the little Bloch-type space Bω,0 to Bμ,0),where ω is a normal function on [0, 1) andμ is a nonnegative function on [0, 1) withμ(tn) ＞ 0for some sequence {tn}n∞n=1(∪) [0, 1) satisfying limn→∞ tn = 1.

关键词： Bloch-type space, composition operator, boundedness, compactness.

Transcriptomic and genetic approaches reveal an essential role of the NAC transcription factor SlNAP1 in the growth and defense response of tomato

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Horticulture Research 2020年第1期7卷 29-39页

作者： Jiao Wang Chenfei Zheng Xiangqi Shao Zhangjian HU Jianxin Li Ping Wang Anran Wang Jingquan Yu Kai Shi Department of Horticulture Zhejiang University866 Yuhangtang Road310058 HangzhouPeople’s Republic of China

With global climate change,plants are frequently being exposed to various stresses,such as pathogen attack,drought,and extreme temperatures.Transcription factors(TFs)play crucial roles in numerous plant biological processes;however,the functions of many tomato(Solanum lycopersicum L.)TFs that regulate plant responses to multiple stresses are largely unknown.Here,using an RNA-seq approach,we identified SlNAP1,a NAC TF-encoding gene,which was strongly induced by various stresses.By generating SlNAP1 transgenic lines and evaluating their responses to biotic and abiotic stresses in tomato,we found that SlNAP1-overexpressing plants showed significantly enhanced defense against two widespread bacterial diseases,leaf speck disease,caused by Pseudomonas syringae pv.tomato(Pst)DC3000,and root-borne bacterial wilt disease,caused by Ralstonia solanacearum.In addition,SlNAP1 overexpression dramatically improved drought tolerance in tomato.Although the SlNAP1-overexpressing plants were shorter than the wild-type plants during the early vegetative stage,eventually,their fruit yield increased by 10.7%.Analysis of different hormone contents revealed a reduced level of physiologically active gibberellins(GAs)and an increased level of salicylic acid(SA)and abscisic acid(ABA)in the SlNAP1-overexpressing plants.Moreover,EMSAs and ChIP-qPCR assays showed that SlNAP1 directly activated the transcription of multiple genes involved in GA deactivation and both SA and ABA biosynthesis.Our findings reveal that SlNAP1 is a positive regulator of the tomato defense response against multiple stresses and thus may be a potential breeding target for improving crop yield and stress resistance.

关键词： breeding drought eventually

亚油酸乙醇胺诱导番茄对灰葡萄孢抗性的作用及机制

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中国农业科学 2022年第9期55卷 1781-1789页

作者：邵淑君胡璋健师恺浙江大学农业与生物技术学院

【背景】灰葡萄孢（Botrytis cinerea）引起的灰霉病是危害番茄（Solanum lycopersicum）的重要病害之一，防治不及时可造成30%—40%减产。目前生产上多以化学防治为主，但存在农产品安全及环境污染的风险。N-酰基乙醇胺（NAE）是植物... 详细信息

【背景】灰葡萄孢（Botrytis cinerea）引起的灰霉病是危害番茄（Solanum lycopersicum）的重要病害之一，防治不及时可造成30%—40%减产。目前生产上多以化学防治为主，但存在农产品安全及环境污染的风险。N-酰基乙醇胺（NAE）是植物体内天然存在的一类脂质生物活性化合物，其在哺乳动物中具有多种免疫功能，但其在植物免疫中的作用和机制尚不清楚。【目的】探讨N-酰基乙醇胺在诱导番茄对灰葡萄孢防御中的作用，为研发番茄灰霉病绿色防控技术提供依据。【方法】将灰葡萄孢分别接种在含有硬脂酰乙醇胺（NAE 18:0）、亚油酸乙醇胺（NAE 18:2）、廿二碳五烯酸乙醇胺（NAE 22:5）的培养基上，观察灰葡萄孢的生长情况。在此基础上，以番茄‘Moneymaker’植株为材料，硬脂酰乙醇胺、亚油酸乙醇胺、廿二碳五烯酸乙醇胺外源处理番茄叶片后接种灰葡萄孢，统计病情指数，测定荧光参数。采用qRT-PCR技术明确亚油酸乙酰胺处理后番茄叶片灰葡萄孢Actin的相对表达量，进一步测定番茄叶片中主要抗病基因PI I、PR-1、NPR1、Nr、ACO1、PYR1a等的相对表达量及茉莉酸（jasmonic acid,JA）、水杨酸（salicylic acid,SA）、乙烯（ethylene,ETH）、脱落酸（abscisic acid,ABA）、生长素（indoleacetic acid,IAA）含量。并以乙烯信号转导突变体植株never ripe(nr)及对照植株Pearson(PB)为材料，在外源亚油酸乙酰胺处理后接种灰葡萄孢，测定番茄叶片叶绿素荧光参数和灰葡萄孢Actin的相对表达量。【结果】体外培养试验结果表明灰葡萄孢生长并不受外源N-酰基乙醇胺的影响，外源施用N-酰基乙醇胺能显著提高番茄植株对灰霉病的抗性，缓解由灰葡萄孢侵染导致的番茄叶片光系统II实际光化学效率（ΦPSII）的下降。3种N-酰基乙醇胺中，亚油酸乙醇胺施用后番茄叶片灰霉病病情指数下降最为明显，灰葡萄孢Actin的相对表达量下调60%，其诱导灰霉病抗性效果最佳。番茄植株接种灰葡萄孢后抗性基因PI I、PR-1、NPR1、Nr、ACO1的表达水平均有不同程度上调。外源亚油酸乙醇胺处理使得番茄响应灰葡萄孢接种后PI I、Nr、ACO1的表达进一步增强，其中乙烯合成基因ACO1的表达水平最高。番茄植株接种灰葡萄孢后叶片水杨酸、茉莉酸、生长素和乙烯含量增加，但外源亚油酸乙醇胺处理并接种灰葡萄孢后只有乙烯含量显著增加。进一步研究发现，番茄乙烯突变体nr植株中，外源亚油酸乙醇胺对灰葡萄孢的抗性诱导作用显著受到抑制。【结论】外源施用亚油酸乙醇胺能够提高番茄内源光合效率和抗病基因的表达及内源激素乙烯的含量，增强番茄植株对灰霉病的抗性，推测其诱导抗性作用可能与乙烯信号路径相关。

关键词：番茄 N-酰基乙醇胺亚油酸乙醇胺灰霉病灰葡萄孢乙烯

The Gleason's problem for some polyharmonic and hyperbolic harmonic function spaces

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Science China Mathematics 2006年第8期49卷 1128-1145页

作者： hu zhangjian TANG Xiaomin Department of Mathematics Huzhou Teachers College Huzhou 313000 China Department of Mathematics Huzhou Teachers College Huzhou 313000 China

Let Ω(∈) Rn be a bounded convex domain with C2 boundary. For 0 ＜ p,q ≤∞ and a normal weight ψ, the mixed norm space Hp,q,ψk,(Ω) consists of all polyharmonic functions f of order k for which the mixed norm ||·||p,q,ψ＜∞.In this paper, we prove that the Gleason's problem (Ω,a,Hp,q,ψk) is always solvable for any reference point a ∈Ω. Also, the Gleason's problem for the polyharmonic ψ-Bloch (little ψ-Bloch) space is solvable. The parallel results for the hyperbolic harmonic mixed norm space are obtained.

关键词： Gleason's problem, mixed norm space, Bloch-type space.

单位球上Bergman空间的Cesàro算子

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数学年刊（A辑） 2005年第2期26卷 219-228页

作者：胡璋剑湖州师范学院数学系浙江湖州313000

对一切p∈(0,∞),Cesaro算子在加权的p次Bergman空间A p(Bn)上有界,但不是紧的,其中Bn是Cn上中的单位球,而是[0,1)上的正规权函数.与Cesaro算子相联系,以解析函数g为符号的积分箅子Rg定义为本文刻画了使算子Rg在A p(Bn)上是有界(或紧)... 详细信息

对一切p∈(0,∞),Cesaro算子在加权的p次Bergman空间A p(Bn)上有界,但不是紧的,其中Bn是Cn上中的单位球,而是[0,1)上的正规权函数.与Cesaro算子相联系,以解析函数g为符号的积分箅子Rg定义为本文刻画了使算子Rg在A p(Bn)上是有界(或紧)的解析函数g的特征.同时,在多圆柱上也能得出类似的结果.

关键词： Cesàro算子 Bergman空间有界紧

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Fock空间及其相关算子

中国科学：数学 2015年第11期45卷 1759-1778页

作者：胡璋剑吕小芬湖州师范学院数学系湖州313000

本文是关于Fock空间及其上相关算子研究的综述,包括Fock空间的定义、Fock空间的Bergman核估计和Carleson测度及其范数等价刻画等基本内容,并且展示了对Fock空间上相关线性算子(如复合算子、广义Ces`aro算子、Toeplitz算子和Hankel算子... 详细信息

本文是关于Fock空间及其上相关算子研究的综述,包括Fock空间的定义、Fock空间的Bergman核估计和Carleson测度及其范数等价刻画等基本内容,并且展示了对Fock空间上相关线性算子(如复合算子、广义Ces`aro算子、Toeplitz算子和Hankel算子及某些线性算子所生成的闭代数)若干特性研究的最新进展,这些特性包括有界性、紧性、Schatten类和Schatten-Herz类等.

关键词： Fock空间 Bergman核 Carleson测度 Toeplitz算子 Hankel算子

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加权Fock空间上的Hankel算子

中国科学：数学 2016年第2期46卷 141-156页

作者：胡璋剑吕小芬湖州师范学院数学系湖州313000

给定1≤p〈∞,本文研究了Hankel算子Hg在加权Fock空间Fφ^p上的有界性和紧性特征,其中φ表示C上不处处为零且？φdA是双倍测度的次调和函数。同时,对2≤p〈∞,本文还讨论了可分Hilbert空间Fφ^2上的Schatten-p类Hankel算子。

关键词： Fock空间 Hankel算子双倍测度